QUESTIONS 1.The definition of "1 atmosphere" is 1013 hPa, the average atmospheric pressure at sea level. But when we computed the mass of the atmosphere, we used a mean atmospheric pressure of 984 hPa. Why? 2.Torricelli used mercury for his barometer, but a column barometer could be constructed using any fluid, with the height of the column measuring atmospheric pressure given by h = P/  fluid g At sea level, with mercury  fluid = 13.6 g cm -3  h = 76 cm with water  fluid = 1.0 g cm -3  h = 1013 cm Now what about using air as a fluid? with air  fluid = 1.2 kg m -3  h = 8.6 km which means that the atmosphere should extend only to 8.6 km, with vacuum above! WHAT IS THE FLAW IN THIS REASONING?

CHAPTER 3: SIMPLE MODELS Define problem of interest Design model; make assumptions needed to simplify equations and make them solvable Evaluate model with observations Apply model: make hypotheses, predictions Improve model, characterize its error The atmospheric evolution of a species X is given by the continuity equation This equation cannot be solved exactly  need to construct model (simplified representation of complex system) Design observational system to test model local change in concentration with time transport (flux divergence; U is wind vector) chemical production and loss (depends on concentrations of other species) emission deposition

TYPES OF SOURCES Natural Surface: terrestrial and marine highly variable in space and time, influenced by season, T, pH, nutrients… eg. oceanic sources estimated by measuring local supersaturation in water and using a model for gas-exchange across interface =f(T, wind velocity….) Natural In situ: eg. lightning (NO x ) N 2  NO x, volcanoes (SO 2, aerosols)  generally smaller than surface sources on global scale but important b/c material is injected into middle/upper troposphere where lifetimes are longer Anthropogenic Surface: eg. mobile, industry, fires  good inventories for combustion products (CO, NO x, SO 2 ) for US and EU Anthropogenic In situ: eg. aircraft, tall stacks Secondary sources: tropospheric photochemistry Injection from the stratosphere: transport of products of UV dissociation (NO x, O 3 ) transported into troposphere (strongest at midlatitudes, important source of NO x in the UT)

TYPES OF SINKS Wet Deposition: falling hydrometeors (rain, snow, sleet) carry trace species to the surface in-cloud nucleation (depending on solubility) scavenging (depends on size, chemical composition)  Soluble and reactive trace gases are more readily removed  Generally assume that depletion is proportional to the conc (1 st order loss) Dry Deposition: gravitational settling; turbulent transport particles > 20 µm  gravity (sedimentation) particles < 1 µm  diffusion  rates depend on reactivity of gas, turbulent transport, stomatal resistance and together define a deposition velocity (v d ) In situ removal: chain-terminating rxn: OH●+HO 2 ●  H 2 O + O 2 change of phase: SO 2  SO 4 2- (gas  dissolved salt) Typical values v d : Particles:0.1-1 cm/s Gases: vary with srf and chemical nature (eg. 1 cm/s for SO 2 )

RESISTANCE MODEL FOR DRY DEPOSITION Deposition Flux: F d = -v d C V d = deposition velocity (m/s) C = concentration C3C3 C2C2 C1C1 C 0 =0 Aerodynamic resistance = r a Quasi-laminar layer resistance = r b Canopy resistance = r c For gases at steady state can relate overall flux to the concentration differences and resistances across the layers: Use a resistance analogy, where r T =v d For particles, assume that canopy resistance is zero (so now C 1 =0), and need to include particle settling (settling velocity=v s ) which operates in parallel with existing resistances. End result: Reference: Seinfeld & Pandis, Chap 19

ONE-BOX MODEL Inflow F in Outflow F out X E Emission Deposition D Chemical production P L Chemical loss Atmospheric “box”; spatial distribution of X within box is not resolved Lifetimes add in parallel: Loss rate constants add in series: (because fluxes add linearly) (turnover time) Flux units usually [mass/time/area]

ASIDE: LIFETIME VS RADIOACTIVE HALF-LIFE Both express characteristic times of decay, what is the relationship? ½ life:

EXAMPLE: GLOBAL BOX MODEL FOR CO 2 reservoirs in PgC, flows in Pg C yr -1 IPCC [2001] atmospheric content (mid 80s) = 730 Pg C of CO 2 annual exchange land = 120 Pg C yr -1 annual exchange ocean= 90 Pg C yr-1 Human Perturbation (now ~816 PgCO 2 )

SPECIAL CASE: SPECIES WITH CONSTANT SOURCE, 1 st ORDER SINK Steady state solution (dm/dt = 0) Initial condition m(0) Characteristic time  = 1/k for reaching steady state decay of initial condition If S, k are constant over t >> , then dm/dt  0 and m  S/k: "steady state"

TWO-BOX MODEL defines spatial gradient between two domains m1m1 m2m2 F 12 F 21 Mass balance equations: If mass exchange between boxes is first-order:  system of two coupled ODEs (or algebraic equations if system is assumed to be at steady state) (similar equation for dm 2 /dt)

Illustrates long time scale for interhemispheric exchange; can use 2-box model to place constraints on sources/sinks in each hemisphere

TWO-BOX MODEL (with loss) m1m1 m2m2 T Lifetimes: If at steady state sinks=sources, so can also write: S1 S2 Q Now if define: α=T/Q, then can say that: Maximum α is 1 (all material from reservoir 1 is transferred to reservoir 2), and therefore turnover time for combined reservoir is the sum of turnover times for individual reservoirs. For other values of α, the turnover time of the combined reservoir is reduced. m o = m 1 +m 2

EULERIAN RESEARCH MODELS SOLVE MASS BALANCE EQUATION IN 3-D ASSEMBLAGE OF GRIDBOXES Solve continuity equation for individual gridboxes Models can presently afford ~ 10 6 gridboxes In global models, this implies a horizontal resolution of km in horizontal and ~ 1 km in vertical Drawbacks: “numerical diffusion”, computational expense The mass balance equation is then the finite-difference approximation of the continuity equation.

EULERIAN MODEL EXAMPLE Summertime Surface Ozone Simulation [Fiore et al., 2002] Here the continuity equation is solved for each 2  x2.5  grid box. They are inherently assumed to be well-mixed

IN EULERIAN APPROACH, DESCRIBING THE EVOLUTION OF A POLLUTION PLUME REQUIRES A LARGE NUMBER OF GRIDBOXES Fire plumes over southern California, 25 Oct A Lagrangian “puff” model offers a much simpler alternative

PUFF MODEL: FOLLOW AIR PARCEL MOVING WITH WIND [X](x o, t o ) [X](x, t) wind In the moving puff, …no transport terms! (they’re implicit in the trajectory) Application to the chemical evolution of an isolated pollution plume: [X] [X] b In pollution plume,

COLUMN MODEL FOR TRANSPORT ACROSS URBAN AIRSHED Temperature inversion (defines “mixing depth”) Emission E In column moving across city, [X] L0 x Solution:

LAGRANGIAN RESEARCH MODELS FOLLOW LARGE NUMBERS OF INDIVIDUAL “PUFFS” C(x, t o ) Concentration field at time t defined by n puffs C(x, t o  t  Individual puff trajectories over time  t ADVANTAGES OVER EULERIAN MODELS: Computational performance (focus puffs on region of interest) No numerical diffusion DISADVANTAGES: Can’t handle mixing between puffs  can’t handle nonlinear processes Spatial coverage by puffs may be inadequate

FLEXPART: A LAGRANGIAN MODEL [Cooper et al., 2005] Retroplume (20 days): Trinidad Head, Bermuda But no chemistry, deposition, convection here x Emissions Map (NO x ) = Region of Influence